Antarctic Whale Project: Single Species
Ben Weinstein
2016-08-05 15:01:14
1 Abstract
2 Descriptive Statistics
2.1 Distance
2.2 Time
2.3 Velocity
2.4 Angles
3 Correlated random walk
Process Model
\[ d_{t} \sim T*d_{t-1} + Normal(0,\Sigma)\] \[ x_t = x_{t-1} + d_{t} \]
3.1 Parameters
For each individual:
\[\theta = \text{Mean turning angle}\] \[\gamma = \text{Move persistence} \]
For both behaviors process variance is: \[ \sigma_{latitude} = 0.1\] \[ \sigma_{longitude} = 0.1\]
3.2 Behavioral States
\[ \text{For each individual i}\] \[ Behavior_1 = \text{traveling}\] \[ Behavior_2 = \text{foraging}\]
\[ \alpha_{i,1,1} = \text{Probability of remaining traveling when traveling}\] \[\alpha_{i,2,1} = \text{Probability of switching from feeding to traveling}\]
\[\begin{matrix} \alpha_{i,1,1} & 1-\alpha_{i,1,1} \\ \alpha_{i,2,1} & 1-\alpha_{i,2,1} \\ \end{matrix} \]
3.3 Environment
Behavioral states are a function of local environmental conditions. The first environmental condition is ocean depth. I then build a function for preferential foraging in shallow waters.
It generally follows the form, conditional on behavior at t -1:
\[Behavior_t \sim Multinomial([\phi_{traveling},\phi_{foraging}])\] \[logit(\phi_{traveling}) = \alpha_{Behavior_{t-1}} + \beta_1 * Ocean_{y[t,]}\] \[logit(\phi_{foraging}) = \alpha_{Behavior_{t-1}} + \beta_2 * Ocean_{y[t,]}\]
3.4 Continious tracks
The transmitter will often go dark for 10 to 12 hours, due to weather, right in the middle of an otherwise good track. The model requires regular intervals to estimate the turning angles and temporal autocorrelation. As a track hits one of these walls, call it the end of a track, and begin a new track once the weather improves. We can remove any micro-tracks that are less than three days. Specify a duration, calculate the number of tracks and the number of removed points. Iteratively.
How did the filter change the extent of tracks?
## user system elapsed
## 191.033 2.010 54261.0613.5 Chains
3.5.1 Compare to priors
3.6 Parameter Summary
## Source: local data frame [10 x 5]
## Groups: parameter [?]
##
## parameter par mean lower upper
## (fctr) (fctr) (dbl) (dbl) (dbl)
## 1 alpha_mu alpha_mu[1] 0.154851383 -0.312184179 0.64179678
## 2 alpha_mu alpha_mu[2] -2.573509702 -3.472531881 -1.66659014
## 3 beta2_mu beta2_mu[1] 0.012593678 0.004049216 0.02323134
## 4 beta2_mu beta2_mu[2] 0.048961383 -0.010272735 0.13109656
## 5 beta_mu beta_mu[1] -0.264739011 -0.590654305 0.03883451
## 6 beta_mu beta_mu[2] 0.431104758 -0.467382077 1.72332873
## 7 gamma gamma[1] 0.879806082 0.832382579 0.93061701
## 8 gamma gamma[2] 0.025357046 0.001438048 0.06500814
## 9 theta theta[1] 0.004732427 -0.027409095 0.03696734
## 10 theta theta[2] 3.360193567 2.255821065 4.36775051
3.7 Behavior and environment
3.7.1 Ocean Depth
3.7.2 Distance to Coast
4 Behavioral Prediction
4.1 Spatial Prediction
4.1.1 Per Animal
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4.2 Log Odds of Feeding
4.2.1 Ocean Depth
4.2.2 Distance From Coast
4.2.3 Interaction
No estimate of uncertainty. 
4.3 Autocorrelation in behavior
4.4 Behavioral description
4.5 Predicted behavior duration
4.6 Location of Behavior
5 Environmental Prediction - Probability of feeding
5.1 Bathymetry
5.1.1 When traveling
5.1.2 When Feeding
5.2 Distance to coast
5.2.1 When traveling
5.2.2 When Feeding
5.3 All variables
5.3.1 When traveling
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5.3.2 When Feeding
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6 Krill Fishery
## used (Mb) gc trigger (Mb) max used (Mb)
## Ncells 1746763 93.3 10367271 553.7 13457386 718.8
## Vcells 231962388 1769.8 459681814 3507.1 382850902 2921.0